Welcome to the wonderful, exciting world of RVing!
Unfortunately, there isn't a "shop manual" like you find in the automotive world. There are generic manuals on how RVs work; 12v, LPG, converters, etc., but, you won't find brand / model specific manuals on how the thing was built, how to take various components apart, etc., just "generic" RV systems books.
Camping World has a selection of these "generic" systems books and other RV related information:
Camping World Bookstore
Depending on how your converter is wired, the A/C, television and most
120v plugs won't work. All the items "required" for living in your TT; furnace, water heater, water pump, refrigerator, 12v lights, stove and oven, should work on your house battery. The problem lies in how long they will work. Most people that "boondock" (camp off the grid) have multiple batteries and various means of re-charging them (solar, generators, even wind turbines) in order to last more than a day or two. Most of the trailer style RVs produced today, unless they have an on-board generator, are designed primarily to have shore power provide most of the "juice" for the components. Short term use, as in stopping at a rest stop or roadside picnic area for instance, is done all the time. Very restful to pull over and be able to "retire" to the rig for potty breaks, lunches or just plain rest.
As for mattresses...what you have discovered is termed an "RV Queen" or a "short queen"...used quite frequently in the RV industry. If memory serves me right, the short is 74" and a regular is 80" or there abouts. There are manufacturers that make "short queens", but, you more than likely won't find them in stock at your local mattress store. Many mattress stores can order them though, so you might want to inquire. Camping World and other RV parts suppliers have access to them, from cheapo replacements all the way up to Select Comfort Sleep Number models. You can also shop around for various "toppers" if you'd rather go that route. Online sources for those are plentiful and you can get a "regular queen" and cut 6" off (more or less) to fit your "short queen" mattress.
I'm sure others will chime with additional ideas...I certainly don't know everything there is to know